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<br />steady or unsteady, pipe or open channel. Furthermore, if open channel <br />flow exists, the relationship between pressure energy and kinetic energy <br />is defined by a double-valued function which requires an additional <br />boundary constraint (critical depth) to satisfy the number of inde- <br />pendent conditions required for a unique solution. In the following <br />discussion of required conditions and equations. the flow is assumed <br />to be steady, open-channel flow. A detailed discussion of classifica- <br /> <br />tion of flow is presented in Chapter 3. Unsteady flow is discussed <br />in Chapter 7. <br />In open channel flow. the potential energy. Yo' is specified as <br />the height of the solid boundary confining the flow above some datum. <br />If the pressure distribution is hydrostatic, the pressure energy, Ply. <br />is the depth of water above the solid boundary. These two energy terms <br />can be added to obtain: <br /> <br />WS = Ply + Y <br />o <br /> <br />(2-10) <br /> <br />where WS is the water surface elevation above the datum, as shown in <br /> <br />fig. 2.01. Equation 2-9 can then be rewritten: <br /> <br />y2 <br />WS + 112 2 = <br />2 2g <br /> <br />WSl <br /> <br />2 <br />1I1Vl <br />+- <br />2g <br /> <br />+ HL <br /> <br />(2-11 ) <br /> <br />An average velocity can be obtained by dividing the flow, Q, by the <br />cross-sectional area, A. Under steady flow conditions, continuity is <br />satisfied because Ql = Q2 = Q, and equation 2-11 can be rewritten as: <br /> <br />ws <br />2 <br /> <br />2 <br />IIQ <br />t. <br />+~ <br />2gJl'2 <br /> <br />= WSl <br /> <br />2 <br />1I1Q <br />+- <br />2 <br />2gAl <br /> <br />+ HL <br /> <br />(2-12) <br /> <br />2.08 <br />